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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_525.104', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.8090169943749475, -0.5877852522924731], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.30901699437494745, 0.9510565162951535], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.30901699437494745, -0.9510565162951535], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 2.438089750056113, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]], [7, [1]]], 'bad_primes': [3, 5, 7], 'central_character': '525.104', 'coeff_info': ['x^10 - 1', '0.809016994374947 + 0.587785252292473*I', '\\\\zeta_{10}'], 'conductor': 525, 'conductor_radical': 105, 'conjugate': 'dirichlet_L_525.419', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^6', 0, 'a^2', 0, 0, 0, 'a^8', 0, 0, 'a^1', 0, 'a^4', 0, 0, 'a^4', 'a^3', 0, 'a^3', 0, 0, 'a^7', 'a^6', 0, 0, 'a^0', 0, 0, 'a^7', 0, 'a^3', 'a^0', 0, 'a^9', 0, 0, 'a^9', 'a^9', 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'189.92469205697525664390183518826', '190.57794878264637605447802187057', '190.79659574495098249108108110064', '191.744045967301828657204071441516', '192.39212207870518099924057397335', '192.81840575312188852774263676889', '193.509400336705030872391389322841', '194.09450848715369448375005908338', '194.83540386090280399916729669627', '195.55499367545575545849197310029', '196.242447199420452208781334939759', '197.07882830732394320167939702798', '197.786070587457384949484662539717', '198.222151872200160621179596199148', '198.86293152828003438893410088427', '199.45151901536715572502004365487'], 'prelabel': '1-525-525.104-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.438089750056113, 'root_angle': 0.48000000000000004, 'root_number': '0.0627905195293133760761782245655+0.998026728428271561952336806863*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.24', 'prec': 14}, 'spectral_label': 'r0-0', 'st_group': 'mu(10)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.639006430459405981475270554238+0.0170939492500021771628489511806*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.52806740021', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.29565945063', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.73275833021', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.438089750056113, 'bad_primes': [3, 5, 7], 'central_character': '525.104', 'conductor': 525, 'conductor_radical': 105, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/525/104'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-525-525.104-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-525-525.104-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.438089750056113, 'root_angle': 0.24000000000000002, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.52806740021', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_525.104', 'Lhash_array': ['dirichlet_L_525.104'], 'label': '1-525-525.104-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/525/104'}
Lfunction data - 1-525-525.104-r0-0-0